need recommendation for watchmaker to repair 1960s cal 561 constellation.

Hi gang.

I just received my 561 cal 1960s SS pie pan which I am in love with. After much research (and having been burned in the past with a redial 50s bumper), I am fairly confident I have an original piece, though the crystal has most likely been replaced.

All works well with the watch. It keeps good time (+15-20 secs per day) and reasonable amplitude on my cheapo timegrapher. Problem is that I cannot wind the watch. I can set the time ok and it works by winding via the automatic winder.

I'm thinking that it may have something to do with the keyless works, but I'm a total noob so I'm probably wrong. Does anyone know of a reputable watchmaker that would service my watch?? I' not looking to polish anything, except the hands maybe as they are looking pretty rusty (hoping that can even be done actually).

THanks for taking the time to read this and for your recommendations. I live in Southern California and would prefer a local watchmaker but am willing to work with someone in the US if they are great. Thanks again.

@GMOG in New Mexico can do it.